A motorist drives for 150 km from City A to City B in 2.5 hr. He makes the return trip in 2.0 hr. Find (a) the average speed for each half of the trip, (b) the average velocity for each half of the trip, (c) the average speed of the entire trip, and (d) the average velocity for the entire trip
150km/2.5hr = 60km/hr
150km/2.0hr = 75km/hr
velocities is the same, but directed.
300km/4.5hr = 66.67km/hr
avg velocity is 0, since no net distance was traveled.
To find the answers, we need to understand the definitions of average speed and average velocity.
Average speed is calculated by dividing the total distance traveled by the total time taken. Average velocity, on the other hand, is calculated by dividing the total displacement (change in position) by the total time taken.
Let's calculate the average speed and average velocity for each half of the trip:
(a) Average speed for each half of the trip:
For the first half of the trip:
Distance = 150 km
Time = 2.5 hours
Average Speed (First Half) = Total Distance / Total Time
Average Speed (First Half) = 150 km / 2.5 hr
Average Speed (First Half) = 60 km/hr
For the second half of the trip:
Distance = 150 km
Time = 2.0 hours
Average Speed (Second Half) = Total Distance / Total Time
Average Speed (Second Half) = 150 km / 2.0 hr
Average Speed (Second Half) = 75 km/hr
(b) Average velocity for each half of the trip:
To calculate average velocity, we need to consider the direction of motion. Since the motorist makes the return trip, the displacement for each half will be zero as the start and end points are the same. Therefore, the average velocities for each half of the trip will also be zero.
(c) Average speed of the entire trip:
To find the average speed for the entire trip, we can simply average the speeds for each half of the trip.
Average Speed (Entire Trip) = (Average Speed (First Half) + Average Speed (Second Half)) / 2
Average Speed (Entire Trip) = (60 km/hr + 75 km/hr) / 2
Average Speed (Entire Trip) = 135 km/hr / 2
Average Speed (Entire Trip) = 67.5 km/hr
(d) Average velocity for the entire trip:
Since the displacement for the entire trip is zero (as the start and end points are the same), the average velocity for the entire trip will also be zero.
Therefore, the answers are:
(a) The average speed for the first half of the trip is 60 km/hr, and for the second half of the trip is 75 km/hr.
(b) The average velocity for each half of the trip is zero.
(c) The average speed of the entire trip is 67.5 km/hr.
(d) The average velocity for the entire trip is zero.